= Height parallelogram identity
{title2=$\widehat h(P+Q)+\widehat h(P-Q)=2\widehat h(P)+2\widehat h(Q)$}
For naive logarithmic $x$-height on an <elliptic curve>, $h_x(P+Q)+h_x(P-Q)=2h_x(P)+2h_x(Q)+O(1)$ uniformly. The unordered pair of sum and difference on the $x$-line defines a bidegree-$(2,2)$ morphism to $\operatorname{Sym}^2\mathbb P^1$, yielding the estimate. Applying it to $2^nP,2^nQ$ and taking the defining limit gives the exact identity for the <canonical height of an elliptic curve>.
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